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Simplifying ln(2x2 + -14) + -1ln(x + 5) = lnx Reorder the terms: ln(-14 + 2x2) + -1ln(x + 5) = lnx (-14 * ln + 2x2 * ln) + -1ln(x + 5) = lnx (-14ln + 2lnx2) + -1ln(x + 5) = lnx Reorder the terms: -14ln + 2lnx2 + -1ln(5 + x) = lnx -14ln + 2lnx2 + (5 * -1ln + x * -1ln) = lnx -14ln + 2lnx2 + (-5ln + -1lnx) = lnx Reorder the terms: -14ln + -5ln + -1lnx + 2lnx2 = lnx Combine like terms: -14ln + -5ln = -19ln -19ln + -1lnx + 2lnx2 = lnx Solving -19ln + -1lnx + 2lnx2 = lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1lnx' to each side of the equation. -19ln + -1lnx + -1lnx + 2lnx2 = lnx + -1lnx Combine like terms: -1lnx + -1lnx = -2lnx -19ln + -2lnx + 2lnx2 = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -19ln + -2lnx + 2lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-19 + -2x + 2x2) = 0Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-19 + -2x + 2x2)' equal to zero and attempt to solve: Simplifying -19 + -2x + 2x2 = 0 Solving -19 + -2x + 2x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '19' to each side of the equation. -19 + -2x + 19 + 2x2 = 0 + 19 Reorder the terms: -19 + 19 + -2x + 2x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -2x + 2x2 = 0 + 19 -2x + 2x2 = 0 + 19 Combine like terms: 0 + 19 = 19 -2x + 2x2 = 19 Add '2x' to each side of the equation. -2x + 2x + 2x2 = 19 + 2x Combine like terms: -2x + 2x = 0 0 + 2x2 = 19 + 2x 2x2 = 19 + 2x Add '-2x2' to each side of the equation. 2x2 + -2x2 = 19 + 2x + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 = 19 + 2x + -2x2 Simplifying 0 = 19 + 2x + -2x2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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